Auto-stereoscopic display apparatus and non-transitory computer readable storage device

1. A non-transitory computer readable storage device for storing an application software adapted to be used for designing an auto-stereoscopic display apparatus, the auto-stereoscopic display apparatus comprising a display area, the display area comprising a display panel and a lens layer, the display panel being configured to receive an image sequence and accordingly display a corresponding image, the display panel comprising a plurality of pixel rows sequentially arranged in a first direction, each one of the pixel rows comprising a plurality of pixels sequentially arranged in a second direction substantially perpendicular to the first direction, and each one of the pixels comprising a plurality of sub-pixels sequentially arranged in the second direction, the lens layer being disposed on the display panel and comprising a plurality of lenticular lenses substantially arranged in the second direction, N successive sub-pixels in each pixel row being corporately covered by one of the lenticular lenses, a ratio of a component of a width in the second direction of each lenticular lens to a width of each sub-pixel in the second direction being configured to a non-integer, an execution of the application software comprising steps of: obtaining a nearest viewing distance of the auto-stereoscopic display apparatus and defining the aforementioned nearest viewing distance as NVD; obtaining a panel width of the display panel in the second direction and defining the aforementioned panel width as L; obtaining an observable angular range of the auto-stereoscopic display apparatus and defining the aforementioned observable angular range as φ; obtaining a width of each one of the sub-pixels in the second direction and defining the aforementioned width as wp; obtaining a minimum outgoing angle difference of each adjacent two lenticular lenses and defining the aforementioned minimum outgoing angle difference as; obtaining an angular spread of each one of the sub-pixels and defining the aforementioned angular spread as γ; obtaining a maximum acceptable angular spread corresponding to the width of the lenticular lens in a space and defining the aforementioned maximum acceptable angular spread as MAlense; and calculating a value N min and a value N max according to the γ, φ, w p , Δθ, MA lense , NVD and L, wherein N min ≦N≦N max ; wherein the software application calculates the value N min based on an equation N min = 1 tan ⁢ ⁢ γ ⁢ ( 2 ⁢ ⁢ tan ⁢ ⁢ φ + L NVD ) - 0.5 .

2. The non-transitory computer readable storage device according to claim 1 , wherein the software application calculates the value N max based on an equation N max = 0.5 ⁢ ⁢ w p ⁢ tan ⁢ ⁢ Δθ + 2 ⁢ ⁢ tan ⁡ ( MA lense / 2 ) ⁢ ( 2 ⁢ ⁢ NVD ⁢ ⁢ tan ⁢ ⁢ φ + L ) w p ⁡ ( 2 ⁢ ⁢ tan ⁢ ⁢ φ + L / NVD - tan ⁢ ⁢ Δθ ) .

3. A non-transitory computer readable storage device for storing an application software adapted to be used for designing an auto-stereoscopic display apparatus, the auto-stereoscopic display apparatus comprising a display area and an eye-tracking system, the display area comprising a display panel and a lens layer, the display panel being configured to receive an image sequence and accordingly display a corresponding image, the display panel comprising a plurality of pixel rows sequentially arranged in a first direction, each one of the pixel rows comprising a plurality of pixels sequentially arranged in a second direction substantially perpendicular to the first direction, and each one of the pixels comprising a plurality of sub-pixels sequentially arranged in the second direction, the lens layer being disposed on the display panel and comprising a plurality of lenticular lenses substantially arranged in the second direction, N successive sub-pixels in each pixel row being corporately covered by one of the lenticular lenses, a ratio of a component of a width in the second direction of each lenticular lens to a width of each sub-pixel in the second direction being configured to a non-integer, the eye-tracking system being configured to track a position of user's eyes, an execution of the application software comprising steps of: obtaining a nearest viewing distance of the auto-stereoscopic display apparatus and defining the aforementioned nearest viewing distance as NVD; obtaining a panel width of a main-lobe observed at the nearest viewing distance and defining the aforementioned panel width as LM; obtaining a width of each one of the sub-pixels in the second direction and defining the aforementioned width as wp; obtaining a minimum outgoing angle difference of each adjacent two lenticular lenses and defining the aforementioned minimum outgoing angle difference as; obtaining an angular spread of each one of the sub-pixels and defining the aforementioned angular spread as γ; obtaining a maximum acceptable angular spread corresponding to the width of the lenticular lens in a space and defining the aforementioned maximum acceptable angular spread as MAlense; and calculating a value N min and a value N max according to the γ, φ, w p , Δθ, MA lense , NVD and L, wherein N min ≦n≦N max ; wherein the software application calculates the value N min based on an equation N min = 1 tan ⁢ ⁢ γ ⁢ ( L M NVD ) - 0.5 .

4. The non-transitory computer readable storage device according to claim 3 , wherein the software application calculates the N max value based on an equation N max = 0.5 ⁢ ⁢ w p ⁢ tan ⁢ ⁢ Δθ + 2 ⁢ ⁢ tan ⁡ ( MA lense / 2 ) ⁢ L M w p ⁡ ( L M / NVD - tan ⁢ ⁢ Δθ ) .

5. The non-transitory computer readable storage device according to claim 3 , wherein the execution of the application software further comprises steps of: obtaining a total equivalent air gap thickness of the optical layer by summing up all the thicknesses of each layer in the optical layer divided by a respective and defining the aforementioned total equivalent air gap thickness of the optical layer as d air ; and calculating a value d max according to the N, φ, w p , Δθ, NVD and L, wherein d max −Δd≦d air ≦d max +Δd and Δd/d max <0.1.

6. The non-transitory computer readable storage device according to claim 5 , wherein the software application calculates the value d max based on an equation d max =(N+0.5)w p NVD/L M .